In description of the holographic dual models, some attempts have
been done to generalize the linear Maxwell electrodynamics to the
nonlinear electrodynamics. The motivation is to examine the
effects of the higher order corrections to the Maxwell field on
the properties and critical temperature of the holographic
superconductors. In this regards, the authors of
[1]}, [2]} analytically studied the holographic
superconductors in the presence of the Born-Infeld (BI) nonlinear
electrodynamics by using the SL eigenvalue problem. They observed
that the higher BI corrections make it harder for the condensation
to form but do not affect the critical phenomena of the system.
Also, the authors of [3]} numerically studied the
non-equilibrium condensation process in a holographic
superconductor when the gauge field is in form of the BI and
Logarithmic one.
